For US citizens there is the global taxation rules. Is there something like that for UK citizens?
I.e. that [new] country will not allow you to become a citizen of it unless you renounce your original one.
What that might actually mean practically, or if you can un-renounce it later, I don't know. [Edit]: Turns out, according to that page, yes, you can do that with some kind of bureaucratic shuffle. Daft - but sometimes these things are.
As for why someone might do it, some do it to ensure they're not at any risk of extra-territorial application of South African laws, especially tax laws.
Members of Parliament have asked South Africa's government whether Musk is still a South African citizen, but that information is protected by South Africa's privacy laws. So we won't ever know for certain unless he reveals it. [1]
[0] https://www.cliffedekkerhofmeyr.com/en/news/publications/202...
The only official response on this has been to refuse to provide information either way based on South Africa's privacy laws. [0]